Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries the full burden of behavioral disclosure, and it discloses nothing: no inputs, no output shape, no mention of whether Bezout coefficients are returned, no error behavior. The tautological text adds no behavioral context of any kind.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

This is under-specification, not conciseness. The repetition 'Extended Gcd: Extended Gcd' is wasted content rather than economical prose, and there is no front-loaded information that helps an agent understand the tool.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

There is no output schema and no description of return values, so an agent cannot know whether the tool returns only the gcd or also the Bezout coefficients and in what arrangement. Given the enormous sibling set and complete absence of annotations, the definition is wholly inadequate for correct selection and invocation.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

With 0 parameters the baseline is 4, and there is nominally nothing to document. However, the tool's name implies two integer operands while the schema is empty, and the description fails to clarify how inputs are supplied (e.g., from conversation context), so it adds no meaning and leaves the invocation mechanism ambiguous.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description 'Extended Gcd: Extended Gcd' is a pure tautology that restates the tool name without adding any information. It does not define what extended GCD computes (gcd plus Bezout coefficients), and it fails to distinguish the tool from the thousands of closely related math siblings (e.g., x402-multiplicative-inverse, x402-pow-mod, x402-chinese-remainder).

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

No guidance whatsoever on when to use this tool versus alternatives. With a catalog of this size containing many number-theory tools, there is no statement of use cases, prerequisites, or exclusions, leaving the agent with zero routing information.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.